Implicit block method for solving neutral delay differential equations

Ishak, Fuziyah; Ramli, Mohd Safwan

doi:10.1063/1.4932463

Cited by 9 publications

(7 citation statements)

References 4 publications

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“…The one-block r-point technique for the 2nd order initial value problem is proposed by Fatunla [15]. A block method will compute simultaneously the solution values at numerous different points on the x axis − of the blocks by Ishak et al [16] and Alkasassbeh and Omar [17]. In this paper, we introduce a new modified 3-point Adams block method of order six for first-order NDDEs.…”

Section: ( ) Dy F X Y a X B Dxmentioning

confidence: 99%

A Modified 3-Point Adams Block Method of the Variable Step Size Strategy for Solving Neutral Delay Differential Equations

Yashkun

Aziz

2019

SJCMS

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A modified 3-point Adams block method of order six (3ABM6) to solve neutral delay differential equations (NDDEs) using variable step size strategy is developed. The approximate solution of the retarded () yx  − and the neutral terms () yx   − of the neutral delay differential equations at the grid points is obtained using the Newton divided difference interpolation technique. The proposed method will approximate the solution in each step using the three-points concurrently. To determine the performance of the proposed method, the maximum errors (MAXERR) and total number of function calls (FNC) will be compared with the method of 2-point order six predictor-corrector. The numerical results show that the 3ABM6 reduces the number of function calls and better accuracy in term of MAXERR.

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Section: ( ) Dy F X Y a X B Dxmentioning

confidence: 99%

A Modified 3-Point Adams Block Method of the Variable Step Size Strategy for Solving Neutral Delay Differential Equations

Yashkun

Aziz

2019

SJCMS

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“…In [7], neutral differential equations are solved using the multistep block method. Other methods of solution include the implicit block method [8], and analyse discontinuities of the derivatives as studied in [9]. Our focus is to obtain symmetries and the corresponding generators of neutral differential equations.…”

Section: Introductionmentioning

confidence: 99%

Lie symmetries of first order neutral differential equations

Lobo¹,

Valaulikar²

2019

J. Appl. Math. Comput. Mech.

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In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this paper, we adopt a different approach and use Taylor's theorem to obtain a Lie type invariance condition and the determining equations for a neutral differential equation. We then split this equation in a manner similar to that of ordinary differential equations to obtain an over-determined system of partial differential equations. These equations are then solved to obtain corresponding infinitesimals, and hence desired equivalent symmetries. We then obtain the symmetry algebra admitted by this neutral differential equation.

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“…In mathematics, the DDEs are differing from ODEs in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. Several numerical methods have been proposed to solve first-order DDEs such as in [1][2][3][4]. However, less attention was made to solve second-order DDEs.…”

Section: Introductionmentioning

confidence: 99%

“…There were few numerical methods that have been proposed for solving ODEs and those methods have been extended to solve DDEs with some modifications in the algorithm. These are some works carried out for solving first-order DDEs using the extended version such as in San et al [1], Ismail et al [2], Radzi et al [3], and Ishak et al [4].…”

Section: Introductionmentioning

confidence: 99%

Solving Second-Order Delay Differential Equations by Direct Adams-Moulton Method

Seong¹,

Majid²,

Ismail³

2013

Mathematical Problems in Engineering

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This paper will consider the implementation of fifth-order direct method in the form of Adams-Moulton method for solving directly second-order delay differential equations (DDEs). The proposed direct method approximates the solutions using constant step size. The delay differential equations will be treated in their original forms without being reduced to systems of first-order ordinary differential equations (ODEs). Numerical results are presented to show that the proposed direct method is suitable for solving second-order delay differential equations.

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Implicit block method for solving neutral delay differential equations

Cited by 9 publications

References 4 publications

A Modified 3-Point Adams Block Method of the Variable Step Size Strategy for Solving Neutral Delay Differential Equations

A Modified 3-Point Adams Block Method of the Variable Step Size Strategy for Solving Neutral Delay Differential Equations

Lie symmetries of first order neutral differential equations

Solving Second-Order Delay Differential Equations by Direct Adams-Moulton Method

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